kinetic molecular theory physical properties of gases: gases have mass gases are easily compressed...

KINETICMOLECULAR

THEORY

Physical Properties of Gases:• Gases have mass• Gases are easily compressed• Gases completely fill their containers (expandability) •Gases diffuse rapidly •Gases exert pressure

Kinetic Molecular Theory

A theory that explains the physical properties of gases by describing

the behavior of the particles

KMT has 5postulates:

#1A gas consists of very small particles that

have mass. (molecules or atoms)

#2Gas particles are

very far apart from each other.

(therefore gases are easily compressed)

#3

Gas particles are in continuous, rapid, random motion.

#4Collisions of gas

particles (with each other and with container) are perfectly elastic(no energy lost)

#5The average energy of the gas particles

depends on the temperature of the

gas.

Measuring gases

• Experimental work in chemistry requires measurements of quantities . Like volume, temperature, pressure and amount. This quantities are variables.

We can measure gases in 4 ways:Measurement Unit

Amount of gas Moles

Volume (V) Liters (L)

Temperature (T) °C, °F, or K

Pressure (P) atm, kPa, Torr, mm Hg, or lb/in2

Temperature (T)

A measurement of the average kinetic energy of a substance, the temperature is related with speed of the molecules of the gas.

Higher temperatures cause gas particles to move faster

K = °C + 273

14°C = ? K14°C + 273 = 287K

To solve gas problems, the temp must always be

in Kelvin (K) !!!

Pressure (P)

The force per unit area on a

surface

Pressure is caused by gas particles slamming into the container’s walls.

•When pressure increases, the number of collisions in a determine time increases

also

VOLUME (V)

• The volume of the gas is the same as the volume of the container. The unit is the Liter (L) = 1000cm3

Units of Pressure:1) atmosphere (atm) 2) Pascal (Pa) 3) millimeters of Mercury (mm Hg)4) Torr5) Pounds per square inch (lb/in2)

1 atm = 101,325 Pa 1 atm= 760 mm Hg = 760 torr

1 atm = 14.70 lb/in2

Bar = 100,000 Pa = 0.9869

Amount of gas

• The mole is the unit for specifying the amount of a sample of matter. You can

relate the number of moles and the mass to the number of

gas particles.

• The pressure exerted by air in the atmosphere is called atmospheric pressure.•VIDEO 1 Weather and air pr

essure•VIDEO 2 What is weather?

Learning CheckA. What is 475 mm Hg expressed in atm? 1) 475 atm 2) 0.625 atm 3) 3.61 x 105 atm

B. The pressure of a tire is measured as 29.4 psi. What is this pressure in mm Hg?

1) 2.00 mm Hg2) 1520 mm Hg3) 22,300 mm Hg

SolutionA. What is 475 mm Hg expressed in atm?

485 mm Hg x 1 atm = 0.625 atm (B) 760 mm Hg

B. The pressure of a tire is measured as 29.4 psi. What is this pressure in mm Hg?29.4 psi x 1.00 atm x 760 mmHg = 1.52 x 103 mmHg 14.7 psi 1.00 atm (B)

Enclosed Gases

• If the container is closed, the pressure inside the container may be different from the atmospheric pressure.• Manometer: Instrument to

measure the pressure in a closed container.

• Determining the pressure in the container will depend on the levels of the Hg on the two sides.• Pressure of the gas in the container is

the same as the atmosphere WHEN THE TWO LEVELS ARE EQUALY HIGH• If the level of mercury is LOWER on the

container side, the pressure in the container is higher than atmosphere.

• The difference between pressures in mmHg is simply the difference between the heights of the two columns.• To find the pressure of the gas in the

container you must add or subtract the difference in pressures to the atmospheric pressure, witch you have separately determined by using a barometer.

• If the mercury level in the container is HIGHER that atmospheric side, the pressure in the container is less than the atmospheric pressure.

• WHEN THE GAS PRESSURE IS HIGHER THAN ATMOSPHERE PRESSURE, THE LEVEL OF MERCURY ON THE SIDE OF THE GAS WILL BE LOWER THAN OPEN ENDED SIDE.

Add differences

• WHEN GAS PRESSURE IS LOWER THAN ATMOSPHERIC PRESSURE, THE LEVEL ON THE SIDE OF THE GAS WILL BE HIGHER THAN OPEN ENDED SIDE..

• Subtract differences

• Pcontainer = Height difference – Atmospheric pressure

• Pcontainer = Height difference + Atmospheric pressure

STOP…collaborate and listen

THE GAS LAWS

• Mathematical representation of the observed relationships among the 4 variables

• BOYLE’S LAW : The pressure- volume Famous experiment involved trapping air,

changing its pressure , and measuring its volume.

If the temperature remains unchanged the product of the pressure times the volume have a constant value K.

• PV = K• The pressure and volume of a sample of gas at

constant temperature are inversely proportional to each other.

• IF PRESSURE INCREASES, VOLUME DECREASES

• IF VOLUME INCREASES, PRESSURE DECREASES

• At same temperature the product of the pressure times the volume of a sample is always the same.

Boyle’s Law

MUST BE AT CONSTANT TEMPERATURE!!

P1V1 = P2V21 = trial 1

2 = after (trial 2)

A gas occupies a volume of 0.458 L at a pressure of 1.01 kPa and temperature of 295 Kelvin. Although the temperature

stays the same, the volume is increased to 0.477 L. What is the new pressure?

0.970 kPa

Charles’ Law

• The relationship between volume gas and its temperature while the pressure and the amount of gas were held constant

• VOLUME INCREASES AS TEMPERATURE INCREASES

• V= K2 T• At constant pressure the volume of a fixed

amount of gas is directly proportional to its absolute temperature.

Charles’ Law

MUST BE AT CONSTANT PRESSURE!!

V1T2 = V2T1

1 = before2 = after

What will be the volume of a gas sample at 309 K if its volume at 215 K is 3.42 L? Assume that pressure is constant.

4.92 L

Gay-Lussac’s Law

MUST BE AT CONSTANT VOLUME!!

1 = before2 = after

2

2

1

1

T

P

T

P

A balloon with a pressure of 0.900 atm is heated from

105 K to 155 K. If volume is held constant, what is the new pressure?

1.33 atm

Combined Gas Law

1 = before 2 = after2

22

1

11

T

VP

T

VP

JUST HOLD ONE QUANTITY CONSTANT!!(take it out of the equation)

The gas in a 0.010 L container has a pressure of 1.39 atmospheres. When the gas is transferred to a 0.017 L container at the same

temperature, what is the pressure of the gas?

0.82 atm

The gas inside a 70.8 mL piston has a temperature of 35.0°C. If the temperature is raised to 100.0°C, what is the new volume of the gas?

85.7 mL

An elastic container is inflated to a volume of 18.0 liters at a pressure of 1.26 atm. The container then expands to a new volume at a pressure of

1.05 atm. What is the new volume?

21.6 liters

Avogadro’s Law

The amount- volume relationship

Equal volumes of gas (at same P and T) contain the same amount of particles

• It states that all gases show the same physical behavior

• A gas with a larger volume must consist of a greater number of particles. As long as the pressure and temperature do not change

• If the amount of gas increases the volume increases

• If the amount of gas decreases the volume decreases

1 mole = 6.02 x 1023 particles

Only works at same P and T

V = K n

1 mole = 22.4 L

Ideal Gas LawThe mother of all gas

laws. It includes everything!

PV = nRT

P = pressure (atm)V = volume (L)n = moles (mol)

R = Gas ConstantT = Temperature

(Kelvin)

PV = nRT

KmolLatm0821.0R

MUST USE THESE UNITS!!!

PV = nRT

If the pressure exerted by a gas at 0.00°C in a volume of 0.0010 L is 5.00 atm, how many moles of gas are present?

2.2 x 10-4 moles

Ideal gases don’t really exist…

…real gases do!

Ideal Gas

A gas that is described by the KMT postulates.

Ideal Gas Law works most of the time.

It does NOT work at very low temperatures and very high pressures.

Dalton’s Law of Partial Pressures

The sum of the partial pressures

of the gases is equal to the total

pressure

Dalton’s Law of Partial Pressures

Ptotal = P1 + P2 + P3 + …

A balloon contains O2 and N2 gas. If the partial pressure of the O2 is 0.75 atm and the partial pressure of the N2 is 0.55 atm, what is the total pressure of

the balloon?

1.30 atm

The gas inside a 70.8 mL can contains H2O(g) and CO2(g) and has a total pressure of 760 mm Hg. If the partial pressure of the H2O is 350 mm Hg, what is the partial

pressure of the CO2?

410 mm Hg

STPStandard Temperature and PressureBehavior of gases depend strongly on temperature and pressure .

0°C or 273 K and 1 atm

How many moles of N2 gas are in a 4.5 L balloon at STP?

0.20 moles

A gas at STP is heated to 55°C. What is the new pressure if volume is held constant?

1.2 atm

A gas tank contains CO2 and O2 gas. What is the total pressure in the tank if the partial pressure of CO2 is 0.45 atm and the partial pressure of O2 is 0.55?

1.00 atm